VENUS. 



pear retrograde from v to iu. Thefe retrograde motions 

 mull neceflarily continue till the planets become ftationary. 

 Hence, a fuperior planet appears retrograde from its fta- 

 tionary point before oppofition to its ftationary point after ; 

 and an inferior planet, from its ftationary poi;:t before in- 

 ferior conjunction to its ftationary point after. 



When Venus appears weft of the fun, that is, from her 

 inferior conjunftion to her fuperior, (he rifes before him, 

 and is called Phofphorus, or Lucifer, or the Morning Jlar ; 

 and when ftie appears eaft of the fun, that is, from her fu- 

 perior conjundlion to her inferior, ftie fets after him, or 

 fliines in the evening after he fets, and is called Hefperiis, or 

 Vefper, or the Evening Jlar : being each in its turn for two 

 hundred and ninety days. 



To delineate the appearance of a planet at any time. 

 Let S be the fun {Jg. II.), E the earth, V Venus, for 

 example ; aV b the plane of illumination perpendicular to 

 S V, cY d the plane of vifion perpendicular to E V, and 

 draw at) perpendicular to c d ; then ^•a is the breadth of 

 the vifible illuminated part, which is projefted by the eye 

 into c 1), the verfed fine of C i) a, or S V Z, for S V f is the 

 complement of each. Now the circle terminating the illu- 

 minated part of the planet, being feen obliquely, appears to 

 be an ellipfe ; therefore, if cmdn reprefent the projeAed 

 hemifphere of Venus next to the earth, mn, c d, two dia- 

 meters perpendicular to each other, and we take c i) = the 

 verfed fine of S V Z, and defcribe the ellipfe rnvn, then c -v 

 is the axis minor, and mcnvm v/\\\ reprefent the vifible 

 enlightened part, as it appears at the earth ; and from the 

 property of the ellipfe, this area varies as c-v. Hence, the 

 vifible enlightened part : the whole difc :: the verfed fine 

 of S V Z : diameter. 



Hence, Mercury and Venus will have the fame phafes 

 from their inferior to their fuperior conjunftion, as the 

 moon has from the new to the full ; and the fame from the 

 fuperior to the inferior conjunftion, as the moon has from 

 the full to the new. Mars will appear gibbous in quadra- 

 tures, as the angle S V Z will then differ confiderably from 

 the two right angles, and confequently the verfed fine will 

 fenfibly differ from the diameter. For Jupiter, Saturn, 

 and the Georgian, the angle S V Z never differs enough 

 from two right angles to make thofe planets appear gibbous, 

 fo that they always appear full-orbed. 



Dr. Halley propofed the following problem : To find 

 the pofition of Venus when brighteft, fuppofing its orbit, 

 and that of the earth, to be circles, having the fun in their 

 centre. Draw Sr perpendicular to EVZ, and put a =: 

 S E, i = S V, .r = E Vj jr = V r ; then * - ;r is the 

 verfed fine of the angle S V Z, which verfed fine varies as 

 the illuminated part ; and as the intenfity of light varies in- 

 verfely as the fquare of its diftance, the quantity of light 



■ A v. u ■ ^-y ^ 



received at the earth varies as = — - 



a'' =: i' + x^ -f- 2 xy ; hence, y 



~b'~ . 



'—, but 



fub- 



ftitute this for y, and we get the quantity of light to be as 



-b"- 



2 b X — a- -\- b'' + x' 



2 *3 



mum ; put the fluxion = o, and we get x =: ^^ 3 a ■ -(- i - 

 — 2 b. Now, i( a = I, b = .72333, as in Dr. Halley's 

 tables, then x = .43036; hence, the angle E S V =r 22° 

 21', but the angle E S V, at the time of the planet's greateft 

 elongation, is 43° 40' ; hence, Venus is brighteft between 

 its inferior conjunftion and its greateft elongation ; alfo, the 

 angle S E V = 39° 44', the elongation of Venus from the 



fun at the fame time, andASVZ=VSE-t-VES = 

 62° 5', the verfed fine of which is 0.53, radius being unity ; 

 hence, the vifible enlightened part : whole difc :: 0.53 : 2 ; 

 Venus, therefore, appears a little more than one-fourth il- 

 luminated, and anfwers to the appearance of the moon when 

 five days old. Her diameter here is about 39", and there- 

 fore the enlightened part is about 10''. 25. At this time, 

 Venus is bright enough to caft a (liadow at night. This 

 fituation happens about 36 days before and after its inferior 

 conjimftion ; for, fuppofing Venus to be in conjunftion with 

 the fun, and when feen from the fun to depart from the 

 earth at the rate of 37' in i day, we have 37' : 22° 21' :: 

 I day : 36 days nearly, the time from conjunftion till Venus 

 is brighteft. 



If we apply this to Mercury, i = .3171, and x = 

 1.00058; hence, the angle ESV = 78° 55''; but the 

 fame angle, at the time of the planet's greateft elongation, 

 is 67° i^TT- Hence, Mercury is brighteft between its 

 greateft elongation and fuperior conjunftion. Alfo, the 

 angle SEV = 22° l8i', the elongation of Mercury at 

 that time. 



When Venus is brighteft, and at the fame time is at its 

 greateft north latitude, it can then be feen with the naked 

 eye at any time of the day, when it is above the horizon ; 

 for when its north latitude is the greateft, it rifes higheft 

 above the horizon, and therefore is more eafily feen, the 

 rays of light having to come through a lefs part of the 

 atmofphere, the higher the body is. This happens once in 

 about eight years, Venus and the earth returning to the 

 fame parts of their orbits after that interval of time. Vince's 

 Elements of Aftronomy. 



The diameter of Venus is to that of the earth as i i-rV to 

 10 nearly, her apparent diameter equal to 59', and real dia- 

 meter equal to 9330 miles ; her apparent diameter, when 

 reduced to the mean diftance of the earth, is, according to . 

 Dr. Herfchel, i8".79, and her real diameter a little largerJ 

 than that of the earth ( fee Planet ) : her horizontal pa- 

 rallax about 30' ; her diftance from the fun is to that of the 

 earth from the fun as 72333 to looooo, and her real dif3 

 tance is 68,891,486 miles ; her excentricity is -rg'^^ths of heif 

 mean diftance from the fun (fee Excentricity) ; the in- 

 clination of her orbit to the plane of the echptic 3° 23' 35" J 

 her periodical courfe round the fun is performed in two 

 hundred and twenty-four days feventeen hours nearly ; and 

 her motion round her own axis in twenty-three hours, orJ 

 according to the obfervations of Bianchini, in twenty-fourT 

 days eight hours : according to Dr. Herfchel, uncertain,! 

 but not fo flow as twenty-four days. See DiameterJ^ 

 Distance, Excentricity, Node, Parallax, and Pe-I 

 RiOD. See alfo Planets, Planetarium, and So/af 

 System. 



Venus, when viewed through a telefcope, is rarely feen 

 to ftiine with a full face, but has phafes juft like thofe of th( 

 moon ; being now gibbous, now horned, &c. and her illu.j 

 mined part is conftantly turned towards the fun, i. e. ifi 

 looks towards the eaft, when Phofphorus ; and towards the; 

 weft, when Hefperus. 



Thefe different phafes of Venus were firft obferved bj 

 Galileo, who thus fulfilled the prediftion of Copernicus ! 

 for when this excellent aftronomer revived the ancient PyJ 

 thagorean fyftem, afferting, that the earth and planet 

 moved round the fun, it was objefted that in fuch a cafe the; 

 phafes of Venus ftiould refemble thofe of the moon ; to 

 which Copernicus replied, that fome time or other that reJ 

 femblance would be found out. Galileo fent an account o^ 

 the firft difcovery of thefe phafes in a letter, written fron 

 Florence in 1611, to WiUiam de Medici, the duke of Tuf-^ 

 cany's ambaffador at Prague ; defiring him to communicate 



ill 



